Does anyone know of a mathematic relationship between ATM implied vols of various expirations?

Ignoring smile-related effects (reasonable if you are concerned only with ATM), look for future events with known calendar times that may affect short-tem volatility and which fall between expirations.

QuoteOriginally posted by: njg1527Does anyone know of a mathematic relationship between ATM implied vols of various expirations?Well, in an interest rate model, you might have a function that pops out, like sigma*(1-Exp[blah])/(2*L) which confers a different "total volatility" at each term in the term structure. That's not really ATM vol, though in the Black Scholes sense.In the case of a stock or stock index, or whatever, I think it's really an economic question, Fermion pointed out. In other words, you will have to postulate the "why" and try to sort out the consequences...